Quantum state smoothing is a technique to construct an estimate of the quantum state at a particular time, conditioned on a measurement record from both before and after that time. The technique assumes that an observer, Alice, monitors part of the environment of a quantum system and that the remaining part of the environment, unobserved by Alice, is measured by a secondary observer, Bob, who may have a choice in how he monitors it. The effect of Bob's measurement choice on the effectiveness of Alice's smoothing has been studied in a number of recent papers. Here we expand upon the Letter which introduced linear Gaussian quantum (LGQ) state smoothing [Phys. Rev. Lett. 122, 190402 (2019)]. In the current paper we provide a more detailed derivation of the LGQ smoothing equations and address an open question about Bob's optimal measurement strategy. Specifically, we develop a simple hypothesis that allows one to approximate the optimal measurement choice for Bob given Alice's measurement choice. By “optimal choice” we mean the choice for Bob that will maximize the purity improvement of Alice's smoothed state compared to her filtered state (an estimated state based only on Alice's past measurement record). The hypothesis, that Bob should choose his measurement so that he observes the back-action on the system from Alice's measurement, seems contrary to one's intuition about quantum state smoothing. Nevertheless, we show that it works even beyond a linear Gaussian setting.

中文翻译：

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线性高斯量子态平滑：了解Alice估计Bob态的最佳解开

量子态平滑是一种根据特定时间之前和之后的测量记录构造特定时间的量子态估计的技术。该技术假设观察者爱丽丝（Alice）监视量子系统的一部分环境，并且该环境的其余部分未被爱丽丝（Alice）观察，由次要观察者鲍勃（Bob）测量，他可以选择监视方式。最近的许多论文中都研究了Bob的测量选择对Alice平滑效果的影响。在这里，我们对引入了线性高斯量子（LGQ）状态平滑的Letter进行扩展。牧师 122，190402（2019）]。在本文中，我们提供了LGQ平滑方程的更详细推导，并针对Bob的最佳测量策略提出了一个未解决的问题。具体来说，我们建立了一个简单的假设，该假设允许在给定Alice的测量选择的情况下，近似于Bob的最佳测量选择。“最佳选择”是指Bob的选择，与她的过滤状态（仅基于Alice过去的测量记录得出的估计状态）相比，它将最大化Alice平滑状态的纯度提高。鲍勃应该选择他的测量，以便他从爱丽丝的测量中观察到系统的反作用这一假设，似乎与人们对量子态平滑的直觉相反。然而，我们证明了它甚至可以在线性高斯设置之外使用。